Study On The Algebraic Type VOF Method With High Resolution Scheme On Unstructured Grids

Compared to the experimental method and theoretical analysis method,numerical simulation for free surface flow has become a mainstream approach in the ship and ocean engineering.Among several numerical methods mentioned in chapter 1.1.2,VOF method is a better choice for simulating free surfaces due to its advantage over other approachs,for instance,VOF method is not only easy to implement but also highly efficient,which can describe strongly nonlinear discontinuous interface's motion and are easily extended to three-dimension.In the framework of unstructured finite volume discretization,VOF method involves several key techniques such as solving the VOF convection transport equation,flux approximation calculation,the reconstruction of the discontinuous interface variable,the calculation of gradient,the surface tension model,and so on.When it comes to VOF equation,it is essentially a convection transport equation,the discretization of convection term will be revelant to the accuracy of interface capturing.However the volume fraction (?) is a discontinuous scalar function in the equation because of the huge density difference between air and water.Therefore,if the convection term cannot be treated properly,a single low-order scheme or high-order scheme may generate pseudo numerical diffusion or numerical dispersion to the sharp and discontinuous interface of scalar function (?),especially in unstructured grids.For the sake of ensuring the high resolution,boundedness and stability of the scalar function,an implicit compressive interface capturing method in 2D unstructured grids is constructed in the paper,including many key techniques.The main content can be summarized as below.(1)First of all,the advantages and disadvantages of geometric reconstruction VOF method and algebraic type VOF method with higher order differencing schemes are discussed in detail.Combined with the advantages of unstructured grids,the conception of solving VOF convection equation based on unstructured grid high accuracy scheme is proposed.Besides,in order to develop the basic two-dimensional unsteady N-S equation solver,we first solve the problem that the solvers can't read Gambit NEU mesh files directly,and construct data structure suitable for triangular meshes,which lays the foundation for the development of solvers.(2)Based on the data structure of unstructured grids,a two-dimensional N-S equation solver is developed,and the solution of the gradient calculation and the upstream node reconstruction is given.A test case of cirular flow around a cylinder is conducted for validation from two aspects.First of all,the feasibility of solver,gradient calculation method,the upstream node reconstruction method and unstructured grid data structure.Secondly,the velocity field is nonconstant and the universal variables(velocity and pressure)are continuous variables in N-S equation.Corresponding to the N-S equation,the velocity can be constant or nonconstant and the universal volume fraction is discontinuous variable of four tests in fifth chapter,which reflects the connection and difference between N-S equation and convection equation.The transmission velocity of VOF equation is from the N-S equation When VOF method is appied to numerical simulation for free surface flow problem,and then the unsteady velocity will be used to solve the fluid volume fraction.(3)At last,compared with continuous variables,discontinuous solutions capturing is more complicated in unstructured grids.Accuracy,boundedness and stability are the evalutation criteria of numerical performance to any method,for which NVDand CBCare introduced for guaranting accuracy and boundedness.Besides,the application of implicit LU-SGS iterative method could enhance the convergence.Based on these key techniques mentioned above,an implicit compressive interface capturing method in 2D unstructured grids is constructed,and convection term is discreted with CICSAM scheme.But,different from the traditional CICSAM method,implicit discretization scheme is carried out in time discretization.On the basis of the technical route,the implementation of the algorithm is accomplished in unstructured grid via Fortran 90 programming.Four pure convection cases are conducted to verify the ability to capture the discontinuous function interface.In terms of accuracy,the new method is totally the same as traditional CICSAM,but its convergence and stability has gained obvious improvement than the latter.In short,the research results are generally in line with the expectation,which laying the foundation for the follow-up study of the VOF method simulating the two-phase flow.